Abstract
This paper investigates some exact and local search methods to solve the traveling salesman problem. The Branch and Bound technique (BABT) is proposed, as an exact method, with two models. In addition, the classical Genetic Algorithm (GA) and Simulated Annealing (SA) are discussed and applied as local search methods. To improve the performance of GA we propose two kinds of improvements for GA; the first is called improved GA (IGA) and the second is Hybrid GA (HGA).
 The IGA gives best results than GA and SA, while the HGA is the best local search method for all within a reasonable time for 5 ≤ n ≤ 2000, where n is the number of visited cities. An effective method of reducing the size of the TSP matrix was proposed with the existence of successive rules. The problem of the total cost of Iraqi cities was also discussed and solved by some methods in addition to local search methods to obtain the optimal solution.
Highlights
The traveling salesman problem (TSP) is a classic combinatorial optimization problem (COP)
We suggest to apply more than one method like BABT1 (IMDM-improved minimum distance method (IMDM)), BABT2: (GRMIMDM), improved GA (IGA), Hybrid GA (HGA), Genetic Algorithm (GA) and Simulated Annealing (SA) for distance cost in the Table-9 and time cost in the Table-10 for n=18
The IMDM serves a good method to solve TSP so it is used as an upper bound (UB) and lower bound (LB) for Branch and Bound Technique (BABT) for different n
Summary
The traveling salesman problem (TSP) is a classic combinatorial optimization problem (COP). Numerous approaches have been proposed and have obtained good solutions They vary in terms of complexity and efficiency and in being able to solve the TSP at various levels of complexity and size (small, medium, and large). Computer simulations demonstrate that the artificial ant colony is capable of generating good solutions to both symmetric and asymmetric instances of the TSP. The method is an example, like simulated annealing, neural networks, and evolutionary computation, of the successful use of a natural metaphor to design an optimization algorithm. Hussain et al (2017) [4] proposed a new crossover operator of genetic algorithm (GA) for TSP to minimize the total distance; this approach has been linked with path representation, which is the most natural way to represent a legal tour.
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